Mathlib Map

Theorems · Definition · category theory

CategoryTheory.Functor.rightAdjoint

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (R : CategoryTheory.Functor D C) → [R.IsLeftAdjoint] → CategoryTheory.Functor C D

A chosen right adjoint to a functor that is a left adjoint.

Defined in
Mathlib.CategoryTheory.Adjunction.Basic
Cited by
5 results in Mathlib
Foundations
Depth 9 from the axioms · uses Classical.choice
Assumes
CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLeftAdjoint
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Sheaf.Γ · cited by 14Sheaf.ΓCategoryTheory.Adjunction.ofIsLeftAdjoint · cited by 9Adjunction.ofIsLeftAdjointCategoryTheory.Functor.isLeftAdjoint_of_iso · cited by 2Functor.isLeftAdjoint_of_…CategoryTheory.isLeftAdjoint_triangle_lift · cited by 1CategoryTheory.isLeftAdjo…CategoryTheory.isLeftAdjoint_iff_hasTerminal_costructuredArrow · cited by 1CategoryTheory.isLeftAdjo…CategoryTheory.isLeftAdjoint_square_lift · cited by 0CategoryTheory.isLeftAdjo…CategoryTheory.Functor.functorCategoryClosed · cited by 0Functor.functorCategoryCl…CategoryTheory.Functor.rightAdjoint.congr_simp · cited by 0rightAdjoint.congr_simpCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.IsLeftAdjoint · cited by 28Functor.IsLeftAdjointCategoryTheory.Functor.IsLeftAdjoint.exists_rightAdjoint · cited by 0IsLeftAdjoint.exists_righ…Functor.rightAdjointCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by8

Results whose statement or proof uses this declaration.